Master this deck with 21 terms through effective study methods.
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A number is divisible by 2 if it is even. A number is divisible by 3 if the sum of its digits is divisible by 3. A number is divisible by 4 if the last two digits form a number that is divisible by 4. A number is divisible by 5 if it ends in 0 or 5. A number is divisible by 9 if the sum of its digits is divisible by 9. A number is divisible by 10 if it ends in 0.
Multiples of a number are obtained by multiplying that number by integers. Factors are numbers that divide another number without leaving a remainder. Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
To find all factor pairs of a whole number, start by dividing the number by integers starting from 1 up to the square root of the number. Each time you find a divisor, pair it with the quotient to form a factor pair.
To find the HCF, list the factors of both numbers and identify the largest common factor. For the LCM, list the multiples of both numbers and find the smallest common multiple. Alternatively, use the relationship: HCF × LCM = Product of the two numbers.
Positive numbers are greater than zero, while negative numbers are less than zero. To compare, place the numbers on a number line; the further to the right, the greater the number. For example, -3 is less than 2.
To add a positive number, move to the right on the number line; to add a negative number, move to the left. For subtraction, add the opposite: subtracting a positive is like adding a negative, and vice versa.
Index notation expresses repeated multiplication of a number. For example, 3 squared is written as 3^2. The square root of a number is the value that, when multiplied by itself, gives the original number, denoted as √x.
To calculate squares, multiply the number by itself. To calculate square roots, determine which number squared equals the original number. For example, the square of 4 is 16, and the square root of 16 is 4.
You can perform operations such as addition, subtraction, multiplication, and division with squares and cubes. For example, (2^2 + 3^2) = 4 + 9 = 13. Cube roots are calculated similarly, finding the number that, when cubed, equals the original.
Factorizing a number into its prime factors can simplify the process of finding square roots and cube roots. For example, the square root of 36 can be found by recognizing that 36 = 6 × 6, thus √36 = 6.
Identify the key information in the problem, set up an equation based on the relationships described, and solve for the unknown using square or cube roots as necessary. Always check your solution by substituting back into the original context.
To estimate, round numbers to the nearest whole number or significant figure, perform the calculation with these rounded numbers, and adjust the result based on the rounding. This provides a quick approximation of the actual answer.
Brackets indicate the order of operations in calculations. According to the order of operations (PEMDAS/BODMAS), calculations within brackets should be performed first to ensure accurate results.
Prime numbers are significant because they are the building blocks of all natural numbers, as every number can be expressed as a product of primes. They have exactly two distinct positive divisors: 1 and themselves.
A number is considered a perfect square if it can be expressed as the square of an integer. For example, 16 is a perfect square because it equals 4^2.
A number is a perfect cube if it can be expressed as the cube of an integer. For example, 27 is a perfect cube because it equals 3^3.
The relationship states that the product of the HCF and LCM of two numbers equals the product of the numbers themselves. This can be expressed as HCF(a, b) × LCM(a, b) = a × b.
A number line is a straight line with a point labeled zero in the center. Positive numbers extend to the right of zero, while negative numbers extend to the left. This visual representation helps in understanding their relative values.
Common mistakes include misapplying the rules of addition and subtraction, such as forgetting that subtracting a negative is equivalent to addition, or incorrectly ordering negative numbers.
Factors and multiples can be applied in various real-life situations such as dividing items into groups (factors) or scheduling events that occur at regular intervals (multiples).
Understanding squares and square roots is crucial in geometry for calculating areas of squares and determining side lengths when given the area, as well as in various applications involving right triangles.